A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and of Plane and Spherical Trigonometry, Together with a Series of Trigonometrical TablesJ. Mawman, 1816 - 294 páginas |
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Página 170
... Complement of an arch is the differ- * The numbers 2 and 3 refer to the Articles of this Introduction : the same may be said of similar references , where the contrary is not specified , throughout the Introduction . ence between that ...
... Complement of an arch is the differ- * The numbers 2 and 3 refer to the Articles of this Introduction : the same may be said of similar references , where the contrary is not specified , throughout the Introduction . ence between that ...
Página 171
... Complement of an angle is , likewise , the differ- ence between that angle and a right angle : and the Sup- plement of an angle is the difference between that angle and two right angles . ( 6. ) DEF . The Sine of an arch is a ...
... Complement of an angle is , likewise , the differ- ence between that angle and a right angle : and the Sup- plement of an angle is the difference between that angle and two right angles . ( 6. ) DEF . The Sine of an arch is a ...
Página 172
... complement . Thus , if AP be any arch , less than a quadrant , of the circle ABCD , having K for its center , let CA and EP be the two diameters passing through A and P ; let the diameter BD , and also the straight lines PF , and EM ...
... complement . Thus , if AP be any arch , less than a quadrant , of the circle ABCD , having K for its center , let CA and EP be the two diameters passing through A and P ; let the diameter BD , and also the straight lines PF , and EM ...
Página 173
... complement , and CBP the supple- ment of AP . Also , BCE is the complement , and CE the supple- ment of the arch ABCE . PF is the sine of AP , and of CBP ; PH is the cosine of AP , and of CBP . AG is the tangent , and KG the secant of ...
... complement , and CBP the supple- ment of AP . Also , BCE is the complement , and CE the supple- ment of the arch ABCE . PF is the sine of AP , and of CBP ; PH is the cosine of AP , and of CBP . AG is the tangent , and KG the secant of ...
Página 182
... complement of the cos ( a + b ) ( 28. ) COR . 1 . arch b . Then , sin ( a c ) - = sin ( a + b - 90 ° ) = ( 19. ) ( 27. ) cos a cos b ( 13. ) cos a cos b , But , sin ( ac ) = sin a cos c — = sin a sin b - cos ( a + b ) = sin a sin b and ...
... complement of the cos ( a + b ) ( 28. ) COR . 1 . arch b . Then , sin ( a c ) - = sin ( a + b - 90 ° ) = ( 19. ) ( 27. ) cos a cos b ( 13. ) cos a cos b , But , sin ( ac ) = sin a cos c — = sin a sin b - cos ( a + b ) = sin a sin b and ...
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Términos y frases comunes
angle opposite base bisect circle EFH circumference co-tangent common section cosine describe a circle describe Art diameter drawn equal and parallel equal arches equal circles equal spheres equal to FE equations Euclid's Elements Find Art fore four right angles given angle given arch given circle given great circle given point given sphere given triangle greater hypotenuse Introd join Art less measure meet oblique angles opposite angle parallel circles perpendicular plane triangle polar distance polar triangle pole Problem PROP proposition quadrantal triangle radius rical triangle right angles right-angled spherical triangle SCHOLIUM semi-circumference shewn side BC sin S sin sine sphe sphere's center sphere's surface spherical angle spherical distance Spherical Geometry spherical polygon spherical tri Spherical Trigonometry straight line tangent Theorem three angles three sides touch the circle triangle ABC trigonometrical functions wherefore
Pasajes populares
Página 53 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 46 - BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles, to which the equal sides are opposite, shall be equal, each to each, viz.
Página iii - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Página 43 - Theorem. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other.
Página 53 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 53 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Página iii - A diameter of a circle is a straight line drawn through the center and terminated both ways by the circumference, as AC in Fig.
Página 132 - If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other, each to each, the two triangles will be equal.
Página 38 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Página 50 - If two angles of a triangle be equal to one another, the sides also which subtend the equal angles shall be equal to one another.